Other mistake: During Dorothy's and the detective's date, they are outside while the boat is moving, yet there is no wind blowing around. Since the ship is moving there should be wing blowing past the two.
Other mistake: When Tom calls Schatze the first time and mentions seeing her ads in magazines, in the following shots while Schatze's on the phone and particularly while she's talking to Pola, we see the milk carton on the table which has tape all the way around it covering its brand name on both sides. (00:19:35)